SPALLATIVE ABLATION: FROM METALS TO DIELECTRICS

AND FROM INFRARED TO X-RAY LASERS

, Petrov Yu.V. , Khokhlov V.A. , ovN.A.Inogam , Anisimov S.I. 1111

,ii ZhakhovskV.V. ,Skobelev I.Yu. , Pikuz T.A. ,Fortov V.E. ,Faenov A.Ya. 22222

,M.Tanaka ,Nishikino M. ,Nishihara K.

,Kishimoto M. ,Kawachi T. ,Kato Y. ,Ishino M. ,Fukuda Y. ,Bulanov S.V.

333

333333

4Shepelev V.V.

Russia 142432, vkaChernogolo Sciences, ofAcademy Russian Physics, lTheoreticafor InstituteLandau 1

Russia 125412, Moscow Sciences, ofAcademy Russian es,TemperaturHigh for InstituteJoint 2

Japan 0215,-619 Kyoto Agency,Energy AtomicJapan Institute, SciencePhoton Kansai3

Russia 123056, Moscow , Sciences ofAcademy Russian Design, AidedComputer for Institute4

velocity sound a is

n.irradiatiolaser aby heated target a oflayer for the timeacoustic /

imelization tion therma-electron

)( fluencen irradiatiolaser ,duration pulselaser

:scales timeThree22 /

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nirradiatiolaser aby heated target inalayer ofdepth the

n irradiatiolaser a ofdepth n attenuatio the

:lengths sticcharacteri Two

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eqsseq

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) unity) oforder the(ofparameter Gruneisen a is (

~layer heated in the pressure pulsesshort For

toup 0 from

layer heated a within increase pressure in the rise gives pulselaser a ofAction

1

Characteristics of a laser irradiation and a matter

metals with ginteractin eV 1~ energy photon n with theirradiatiolaser optical )1 L

torssemiconduc with ginteractin eV 1~ n irradiatiolaser optical 2) L

sdielectric with eV 1~ n irradiatiolaser optical ofn interactio 3) L

sdielectric and torssemiconduc metals,

onto actingn irradiatio rays-Xsoft or t ultraviole hard 4)

nm 250~Au for nm, 100~ AlFor

)(

ydiffusivitheat electron

en wh 2

3

,2

, en wh2

)(

nm 2010~~

F

2/1

2

F

5/1

5/2

TT

eT

e

ee

eBeBe

T

eeTeB

eT

skinatt

dd

ttd

c

Tknk

d

TETkFFd

dd

metals with ginteractin eV 1~ n irradiatiolaser Optical )1 L

T

e

attT

T

d

dd

Fd

2 vspeed supersonic a with propagates heat waveEletron

tyconductiviheat electron high

andnsfer energy traion -electron the todue

fluencelaser upon thet independeny practicall is

ehw

metals with ginteractin eV 1~ n irradiatiolaser Optical L

considered becan

.emperatureelectron t on the re temperatumelting of dependence

as wellas eV) tensseveral to(up

emperatureelectron thigh very upon the spectraphonon a of dependence the

melting the toUp

layer. e within thexists metal a of state unique a At

Teq dtt

Unique state of metals under the action of femtosecond laser

irradiation. Phonon spectra of a metal with a hot electrons

within the Thomas-Fermi approach (simple metals)

The only state suitable to investigate the lattice

dynamics at electron temperatures up to several tens eV

) v,,(2

),v,(2

),v(

spectraPhonon

0.2parameter lattice Reduced

crystal bcc

3/13/4

,s

ZZTZZ

TZ

T

a

es

ese

kk

Unique state of metals under the action of femtosecond laser

irradiation. Dependence of a melting temperature of a simple

metal on the electron temperature

)v,(

)v,()v,(

re temperatuMelting

2.0 1.6; 1.2; ;6.0

constant lattice Reduced

crystal bcc

3/43/7

3/7

3/1

ZTZTZ

TTZTT

Zaa

a

em

emem

The only state suitable to investigate dependence of a

melting on the electron temperatures

0 2 4 6

t, ps

0.84

0.88

0.92

0.96

1

R /

Ro :

Re

fle

ctivity o

f pro

b f

sL

P n

orm

aliz

ed

to

Re

flectivity b

efo

re P

um

p

Al, Fabs = 65 mJ / cm2, Finc = 0.75 J / cm2

alpha = 30, b = 3.5

The black curve with markers=experiment

The blue curve = 2Tgd with b=0The red curve = 2Tgd with b=3.5

where nu = nuei + nuee

nuee = b*(EF/hbar)(Te/TF)2

DETERMINING INTRINSIC PARAMETERS OF METALS.

AL, INFLUENCE OF ELECTRON-ELECTRON INTERACTIONS

ONTO THE REFLECTIVITY

eeeie

F

eBFee

Tkb

2

Evolution of the phase shift of reflected light,

caused by the melting kinetics (Al)

• Phase shift with respect to the reflection from the cold aluminum state

• Calculations and experiments are in a good agreement

0 2 4 6

t, ps

0

2

4

6

P

si,

nm

- p

ha

se

diffe

ren

ce

be

twe

en

th

e c

urr

en

t p

ha

se

an

d th

e p

ha

se

befo

re p

um

p

Al, Fabs = 65 mJ / cm2, Finc = 0.75 J / cm2

alpha = 30*1017 (erg/s)/(cm3 K)

experiment

bopt=0, meff = 1.6

bopt=3.5, meff=1.2

Melting kinetics is described accurately:because 2Tgd dependence agrees wellwith experiment expansion

crater

Evolution of Optical Parameters after the Pump Impact

Au• Changes in the reflectivity and the phase of reflected

probe light after the pump action

eV1

• Gold

• The upper three curves are phases

• The bottom curves present the drop

in the normalized reflection

coefficient R/Ro

• Fabl is an ablation threshold

• Finc is incident fluence of the

chromium-forsterite laser

tau_L=100 fs, lambda=1240 nm (1

eV)

• The pump operates at the first

harmonics :

• The probe operates at the second

harmonics :

• The red rectangular presents

duration tau_L of the pump pulse

• It should be emphasized that

optical changes are fast :

compare duration tau_L and rise

time for R and

eV2

Exitation of 5d-electrons into 6s-6p-bands

0 2 4 6 8 10

Te, eV

1

2

3

4

5

Nu

mb

er

of e

lectr

on

s in

6s +

6p

zo

ne

s

Au

• Increase of the number of electrons in 6s-p bands

-0.4 -0.2 0 0.2 0.4 0.6

X axis (kJ/mol)

0

50

100

Y a

xis

(kJ/m

ol)

DETERMINING INTRINSIC PARAMETERS OF METALS.

Au

d

Tk

xBatis

eBe

dx

xx

xk

M

m

m

mnZ

s

0

2

0

2

2

1)(

12

.

dx

eexx

xk

M

m

m

mnZ

eBeB Tk

x

Tk

Batid

12

21

0

2

0

2

2

1

1

1

1

)(

12

.

(2007) Celli V. Zhigilei,L.V. Lin, Z.

101.2)eV2( ,106.1)eV1( 1717

K W/m10 α, 317

eV , Te

ACOUSTIC DECAY OF THE PRESSURIZED

BY THE LASER IRRADIATION TARGET LAYER

reflected) andleft (right, waves threeof composed is profile pressurecurrent The c)

wavereflected theproducesboundary aon Left wave b)

heatinglaser a todue layer sticcharacteri e within th pressure and re temperatua of Increase a) TdpT

Short pulse laser irradiation results in the spallative ablation

INCREASE OF THE POSITIVE AND NEGATIVE PRESSURES

WITH THE FLUENCE INCREASE

Two-temperature hydrodynamics approach

)()/(

)()/(

0

0

0

00

0000

0

0

0

ieii

ieeee

TTx

up

t

E

QTTx

up

x

T

xt

E

x

p

t

u

Hydrodynamics equations describe:

Heating of ion subsystem via energy transfer from hot electrons to ions (term

with the coefficient )

Expansion of electron thermal wave into the bulk target (the -

term – electron heat conduction in the equation for the energy of electrons)

Expansion of a hot target matter

Initial state of a crystal for two-temperature hydrodynamics.

Pulse has a gaussian temporal form.

)/exp()( 22

0 tFtF

3/ , cmg GPap ,

skmv / , KT ,

nmx ,

fs

tFtF

100

)/exp()( 22

0

Target parameters at instant t=0, corresponding to the

fluence maximum

Target parameters immediately at the end of laser pulse

(t=0.3ps)

Parameters of a target at the instant of the equalization of

electron and ion temperatures Te=Ti

1. Two-temperature hydrodynamics provides adequate

initial conditions for further used molecular dynamics

simulation of laser ablation of metals.

2. Molecular dynamics simulation with many-body

potentials of metals is more adequate to describe the

ablation pattern late in a time when phase transitions

occur.

))(1/()()(

)1/())(()(

))()(())(/1()(

, ,

32

2

222

1

4

2

321

6

3

610

2

2

1

2

1

rcrrcrn

nbnbbnbnF

xaxxxxaxrV

raxrax

c

cc

cc

ik

iki

i

ij

iji

rnn

nFrVU )()(

Embedded atom potential for aluminum

The same potential will be used for AlF

nm 6875.0cr Is a cut0ff radius, other parameters are obtained from the

minimization procedure for a sum of deviations from the

experimental data at normal conditions and from the cold

stretching pressure evaluated by ABINIT density functional

code

Gaussian Focal Spot

and Final Morphology of Irradiated Area

• There are significant effects

connected with existence of foam

• The foam continues to decelerate

cupola after nucleation. In larger

objects this is impossible since

surface tension and existence of

foam are dynamically insignificant

against inertial force

• The foam is the reason for

appearance of the nanomodulations

at the surface of the cupola

• If solidification is fast enough

remnants of the foam remain frozen

around the crater and in the bottom of

the crater

thermomechanical

ablation threshold

cavitation threshold

melting threshold

evaporation

surface profile long after irradiation

Fa

Gaussian fluence F(r)

Fc

Fm

debris

crater

rim

frozen bubbles

Nucleation and Formation of a Foam

• Figure shows matter motion and its thermodynamic phase composition after action of Gaussian laser beam with maximum intensity at the middle vertical straight line.

• In metals and semiconductors nucleation under stretching takes place inside the molten layer (cavitation)

• Action of Gaussian in transverse plane laser beam creates nonhomogeneous heating – absorbed fluence depends on radius r from the beam axis. It results in the formation of thin liquid runaway layer (cupola) above the focal spot at a surface. Thickness of the cupola is a function of the local value Fabs(r) – it is thinner in the central region where Fabs is larger. There is a liquid-vapor foam under the cupola. Foam region becomes thicker near the central axis. The bottom of the future crater is located under the liquid layer, separated from the bulk matter by the melting-solidification front

Molecular dynamics simulation of the ablation pattern

above the ablation threshold. Formation of the spalled

cupola

cS t / dT = 0.72 2.1 3.7

y

AM

M

E

z

z

(a)

(b) (c)

crit

Cr

Cr

1

2

1

2

0 0'

0A A MME

ivv

E

Fm

Fa

Fev

Fcrit

Fc c

iii iii

Time dependence of the spalled layer pattern

Formation of the spalled cupola under the action

of laser pulse with spatial Gaussian fluence

profile

Ablation pattern for different intstants

Newton rings

Golden target. Pump light angle equals 45 degrees. The interval between the top

of parabolic cupola-shaped spallation plate and target surface equals 1800 nm.

Мolecular dynamics simulation of the laser

ablation of bulk aluminum

The wide Al target with cross section LyxLz=122x14 nm2 heated up to the T0(0)=5 kK at the small

heated depth dT =18.6 nm. The total simulation time is 153.5 ps.

0.1ps pump

torssemiconduc with ginteractin eV 1~ n irradiatiolaser Optical 2) L

metalsin that similar to depthscrater

and hresholdablation t fluence the torise giving place takestorssemiconducin ablation Spallative

metalsin asorder same theofstrength materialt significan a have and

hot t tooaren' torssemiconduc so electrons, exite torequied isenergy small a gap narrow the toDue

increasessharply eunit volumper energy laser absorbed and valuesmetallic to

dropsdepth absorbtion theelectrons, conduction ofdensity plasma critical a achievingWhen

processes. tunnelandphoton -multi

n, transitiointerbanddirect through band conduction to valencefrom electrons exitesn irradiatioLaser

ATTENUATION DEPTH OF AL AND SI IN DEPENDENCE ON LASER

LIGHT WAVELENGTH

ATTENUATION DEPTH OF AL AND SI IN DEPENDENCE ON LASER

LIGHT WAVELENGTH (shorter wavelengths)

Pictures of the Newtonring-like structure on sixdifferent materials:

1. silicon2. gallium arsenide3. aluminum4. gold5. magnesium6. mercury

K. Sokolowski-Tinten et al.Applied Surface Science 127–129 (1998) pp.755–760

Newton rings as a

manifestation of

spallative ablation

(1) (2)

(3)

(5)

(4)

(6)

sdielectric with eV 1~ n irradiatiolaser optical ofn Interactio 3) L

ablation spallative a toleading ,, torssemiconducin while

, thresholdbreakdown optical thesdielectricin sother word By the

expansion gas as looks state thisfromexpansion icalHydrodynam

strength. material small negligibly with statehot a into transfersDielectric

electrons. conduction of

density critical a achieve energy to large anessesary isit gap widea toDue

ablopt

ablopt

FF

FF

eaeaccBeaat

eeeeee

s

eea

s

e

T

ereceimp

i

e

AEEnnkCEdt

dTC

TnEEunEEQdt

dE

td

FQnn

u

Q

dt

dn

, cm106 , 6 ,

)2/3( , ,

)/exp( ,

3-22

2

223

2

Evolution of the parameters of a LiF matter within the heated layer Td

sdielectric and torssemiconduc metals,

onto actingn irradiatio rays-Xsoft or t ultraviole Hard 4)

eB

Fi

impec

Fi

impe

Fi

imp

Li

impec

Li

impe

Li

imp

Tk

en

en

/s][cm 18.0

)1/(107.0v ,v

/s][cm 5.1

)1/(1011v ,v

38

38

ELECTRON IMPACT IONIZATION FREQUENCIES

eV 14

THE THREE-BODY RECOMBINATION RATE

P)P( 15 , 18.0 1.6 , 1 :F

S)S( 1 , 5.1 ,12 , 0 :Li

1)(

, )(12

)(410

32

0

12

0

2/1

1

0

0

2/3

32/38

i

i

eB

i

i

Brec

QAl

QAl

AG

TkG

g

g

l

Q

E

Rya

ELECTRON-ATOM ENERGY EXCHANGE RATE

1-11

216

s 10)2010(v3 with

Then

cm 10)147( nm 20.015.0

3v

frequency collision atom-electronv

collision onein

atom oelectron t from nsferredenergy tra average the32

33

e wher,

ceae

Li

ea

eaLi

eBe

ceaeea

e

Li

eB

Li

eeaa

nM

mAAEE

r

m

Tk

n

EM

mTk

M

m

nE

Evolution of the parameters of a LiF matter within the heated layer Td

;s102 eV, 25 :1 ;s109 eV, 14 :2 ;s102 eV, 14 :1

re temperatuatomic theof Increase (c)

cooling a-e thebecause decreases and

ionrecombinat and )( sourcelaser a ofaction the viaincreases emperatureElectron t (b)

ionrecombinat a todue isdecay andation photoioniz the todue is ofGrowth

. populationelectron free ofion Concentrat a)

1-11

2

1-11

2

1-11

2 AuAuAu

tQ

n

iii

e

nm28 ,ps 7 ,mJ/cm 10 3 TdF

TT

atatatea

at

eeeea

e

d

xt

d

FQ

x

T

xx

upE

E

t

x

T

xx

upEQ

E

t

0

2

2

0000

00

0000

000

exp

TEMPORAL AND SPATIAL EVOLUTION OF THE PARAMETERS OF A MATTER

AT THE ACOUSTIC STAGE

3

CRYSTALLINE LITHIUM FLUORIDE

33

AlLiF

Molar mass 25.939 g/mol 26.981 g/mol

Density 2.635 g/cm 2.70 g/cm

Melting point 1118 K 931 К

Crystal structure NaCl-type fcc fcc

Isothermic compressibility-111 Pa 103.1 -111 Pa 103.1

1113 s102 ,nm28 ,ps 7 ,mJ/cm 10

n wave;rarafactio a of tail tensilea ofFormation

AdF T

LiF

EVOLUTION OF PRESSURE PROFILES IN LIF CRYSTAL CREATED BY

THE ABSORBTION OF XUV-PULSE.

Molecular dynamics simulation

TEMPERATURE PROFILES IN LIF

CONCLUSION

1.Spallative (thermomechanical) ablation is the

universal mechanism of a matter removal from the

condensed targets by short laser irradiation equally

existing for metals, semiconductors and dielectrics

2. Spallative ablation for dielectrics takes place for

shorter light wavelength than in metals and

semiconducors

K W/m10 α, 317

eV , Te

The interference pattern from Al target for a pump pulse fluence 0.96 J/cm .

The left figure was obtained by using Linnik microinterferometer at time delay

700 ps after pump. The right figure is a theoretical prediction based on Fresnel

formulae.

Experimental results on aluminum.

Comparison with the theoretical calculation

2

Experimental results on gold

and the comparison with the theory

The interference pattern from Au target for a pump pulse

fluence 2.86 J/cm2 (above the evaporation threshold). The

central part of cupola was destroyed. The right figure is a

theoretical prediction based on Fresnel formulae.

Femtosecond laser irradiation:

1.Creates unique state of matter when interacting

with metals and semiconductors

2. Originates in the specific forms of ablation of

these materials

3. Forms specific postablation structures in a

target

4. Provides the means of probing these

phenomena by itself

DETERMINING INTRINSIC PARAMETERS OF METALS.

Dielectric permittivity of Al

• At room temperature there is a significant contribution to from interband transitions between parallel bands (Palik, 1998; Miller, 1969)

• This contribution diminishes during melting (Miller,1969) and at a high electron collision frequency (Ashcroft, Sturm, 1971), thus the Drude term dominates in .

• is defined by Z and :

• Z=3 (this value defines a frequency of plasma oscillations ): there is no additional

excitations of electrons into s-band at our temperatures (Te is less than 10 eV)

• Important fact is: electron-electron collisions seems weakly contribute to even when crystalline lattice still exists after pump illumination. This means that in a rather hot electron gas the Umklapp contribution is weak

• Therefore only electron-ion collision frequency may influence .

• At early stage and even late in a time ion temperature Ti is limited by values less than 10 kK at our range of fluences Ti[kK] 2.5*(Fabs/65[mJ/cm2]), (Fabs)abl = 65 mJ/cm2, Fabs is absorbed fluence, (Fabs)abl is ablation threshold on absorbed fluence

• weakly depends on Te

• is less than 1 at the early stage, therefore there is no significant changes in

of Al at the early stage caused by the pump heating

22

2

22

2

1

pp

Drude i

Drude

p

ei Drude

ei /ei

Drude

K W/m, κ s

eV , Te

Transformation of electron d-band of Au when the electron

temperature increases from the room temperature to the values

about 5 eV. Schematic presentation of the density of state.

Crystalline lattice remains cold up to the instants ~ 1 ps)

E

E

6s

6s

EF

EF

5d

5d

probe2 eV

probe2 eV

RT

2T, Te ~ 5-10 eV

Exitation of 5d-electrons into 6s-6p-bands

• Equation for the chemical potential

)exp(1

)exp(1

ln

1exp

2

2

1

0

3

2

e

e

e

e

kT

kTgkT

kTx

dxxmkT

nzdzsz

zs is a number of electrons in 6s-p-bands per atom

zd – the number of electrons in 6s-p-bands per atom

n is the atom density

g – the average density of state in 5d-band

Band structure, plasma frequency and electron

collision frequency

iZ

20

)/(1

)/(2110,1)/(212.1

r

Z

2)/(1

2115.14,112119

• Describing the experimental data on a phase shift and raflectivity

• Z=Ne6s ~ (2-4) для Te ~ (5-10) eV

1,1at)/(21

),eV2(103:Probe

0

2

15

effpl mZ

32~)/(

3~

Z

E

E

6s

6s

EF

EF

5d

5d

probe2 eV

probe2 eV

RT

2T, Te ~ 5-10 eV

Dielectric permittivity of Au

• , calculations show that d term is

small in comparison with the s term at the

considered range 0<Te<10 eV

• At small it is due to the small number of holes

= Z-1 in the d-band, ( Z is the number of

electrons per ion in 6s, 6p bands)

• At the elevated Te [3-6 eV] , but the

electron-ion collision frequency for the d electrons

is high – again is small

ds

eT

hN

1~hN

d

K W/m, κd

eV , Te

Comparison of the change of dielectric permittivity

of Al and Au with electron temperature growth

• Values of Te/TF are similar for Al and Au compared here but the 2T state remains hidden in Al (weak manifestation in eps) while the Te rise obviously manifests itself in case of gold (2T=Two-Temperature)

Re1

• Change in at the early stage. They are initiated by the pump action

• Relative values of are shown –normalization to the R.T. values corresponding to the state before the pump

1

Re1

pressure a of growths temporalacoustics and kinetics of Comparison (c)

pressure total the toonscontributi atomic and electronic of Comparison )b(

and sfor variou pressure Total (a) 2 Aui

LiF

I. Femtosecond laser irradiation creates the unique state of

matter

114

s s10 , ν

eV , Te

Electron-ion collision frequency in Au (s-electrons)

114

d s10 , ν

eV , Te

Electron-ion collision frequency in Au (d-electrons)

2T dielectric permittivity of Au : Z and

collision frequencies for• Z grows with Te as a result of excitation of d-electrons

• Question about NU for epsilon:

• (1) es—ions

• (2) es—es (Umklapp)

• (3) es---ed

• NU for epsilon and NU for kappa

are different:

NUeps=1+2Umklapp+3, while

NUkappa=1+2all+3

• For Au in our conditions (1) is

rather important; (2,3) seems are

unimportant

• They explain fast changes in eps